摘要翻译：
大多数长记忆预测研究都假设记忆是由分数差分算子产生的。我们认为，最常被引用的关于长记忆存在的理论论点并不意味着分数差分算子，并评估了自回归分数积分移动平均(ARFIMA)$模型在预测由非分数过程产生的具有长记忆序列时的性能。我们发现高阶自回归$(AR)$模型在短视距下产生类似或优于$ARFIMA$模型的预测性能。尽管如此，随着预测范围的增加，$ARFIMA$模型往往在预测业绩中占据主导地位。因此，$ARFIMA$模型非常适合于长记忆过程的预测，而不管长记忆的产生机制如何，特别是对中长期的预测。此外，我们还分析了对高阶自回归($HAR$)模型施加限制的异构自回归($HAR$)模型的预测性能。我们发现，在某些情况下，$HAR$模型所施加的结构产生了比同阶$AR$模型更好的长时预测，而短时预测的价格则较低。我们的结果对气候计量经济学和金融计量经济学模型等在不同预测水平下处理长记忆序列具有一定的启示意义。我们在一个例子中表明，当短记忆自回归移动平均$(ARMA)$模型在预测未来一个月的标准普尔500已实现方差时，给出了最好的性能，而$ARFIMA$模型在较长的预测范围内给出了最好的性能。
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英文标题：
《On Long Memory Origins and Forecast Horizons》
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作者：
J. Eduardo Vera-Vald\'es
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最新提交年份：
2017
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Most long memory forecasting studies assume that the memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator, and assess the performance of the autoregressive fractionally integrated moving average $(ARFIMA)$ model when forecasting series with long memory generated by nonfractional processes. We find that high-order autoregressive $(AR)$ models produce similar or superior forecast performance than $ARFIMA$ models at short horizons. Nonetheless, as the forecast horizon increases, the $ARFIMA$ models tend to dominate in forecast performance. Hence, $ARFIMA$ models are well suited for forecasts of long memory processes regardless of the long memory generating mechanism, particularly for medium and long forecast horizons. Additionally, we analyse the forecasting performance of the heterogeneous autoregressive ($HAR$) model which imposes restrictions on high-order $AR$ models. We find that the structure imposed by the $HAR$ model produces better long horizon forecasts than $AR$ models of the same order, at the price of inferior short horizon forecasts in some cases. Our results have implications for, among others, Climate Econometrics and Financial Econometrics models dealing with long memory series at different forecast horizons. We show in an example that while a short memory autoregressive moving average $(ARMA)$ model gives the best performance when forecasting the Realized Variance of the S\&P 500 up to a month ahead, the $ARFIMA$ model gives the best performance for longer forecast horizons.
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PDF链接：
https://arxiv.org/pdf/1712.08057